Skills Practice Skills Practice for Lesson 10.1 Name Date Water Balloons Polynomials and Polynomial Functions Vocabulary Match each key term to its corresponding definition. 1. A polynomial written with the terms in descending order, starting with the term with the greatest degree and ending with the term with the least degree. 2. In a polynomial in one variable, it is the exponent of that variable with the largest numerical value. a. polynomial b. term 10 3. An expression that consists of a single term that is either a constant, a variable, or a product of a constant and one or more variables. It is a polynomial with one term. c. coefficient 4. A method of determining whether an equation is a function. It states that an equation is a function if you can pass a vertical line through any part of the graph of the equation and the line intersects the graph at most one time. d. degree 5. A polynomial with exactly two terms. e. monomial 6. The number multiplying one or more variables in a term. 7. The parts of a polynomial that are added. They may be a number, a variable, or a product of a number and a variable (or variables). 8. An expression of the form a 0 a 1 x a 2 x 2... a n x n, where the coefficients (a 0, a 1, a 2,...) are real numbers or complex numbers and the exponents are non-negative integers. f. binomial g. trinomial h. standard form 9. A polynomial that consists of three terms. i. vertical line test Chapter 10 Skills Practice 637
Problem Set Name the terms and coefficients of each polynomial. 1. 3x 9 The terms of 3x 9 are 3x and 9. The coefficient of 3x 9 is 3. 2. 4x 2 5x 0 3. 10a 3 8a 5 4. 6a 4 7a 3 3 5. b 4 b 2 4b 3 6. b 6 9b 4 12b 2 b 1 Classify each polynomial below by its number of terms. 7. 6x 2 x 9 8. x 2 8x 11 The polynomial is a trinomial. 9. 8x 10. 10x 11. 3x 1 12. x 17 638 Chapter 10 Skills Practice
Name Date 13. 2x 3 14. x 10 15. 31x 2 17x 9 16. 20x 2 43x 7 Classify each polynomial by its degree. 17. y 3 The degree of the polynomial is 1. The polynomial is a linear expression. 18. y 4 19. 3y 2 6y 9 10 20. 2y 2 8 21. 9 22. 24 23. y 3 27 24. y 3 5y 2 10y 15 25. 10y 2 10y 5 27y 26. 7y 4 14y 2 y 6 Rewrite each polynomial in standard form. 27. 10 3x 2 18x 28. 20x 6 2x 2 3x 2 18x 10 29. 84x 31x 2 x 3 19 30. 72 9x 2 81x 3x 3 Chapter 10 Skills Practice 639
31. x 3 32. 2x 30 33. 4x 7 3x 2 x 6 9x 4 34. 7x 9 18x 10 8x 4 x 35. 24 33x 8 x 36. 100 2x 2 8x 9 0 Use the Vertical Line Test to determine whether the equation represented by each graph is a function. 37. y 38. 4 y 4 3 2 1 4 3 2 1 1 2 3 4 x 1 2 3 4 3 2 1 1 1 2 3 4 5 6 7 x 1 2 3 4 No vertical line intersects the graph in more than one point. The graph passes the Vertical Line Test. The equation represented is a function. 39. y 40. 4 3 2 1 4 3 2 1 1 2 3 4 x 1 2 y 4 3 2 1 4 3 2 1 1 2 3 4 x 1 2 3 3 4 4 640 Chapter 10 Skills Practice
Skills Practice Skills Practice for Lesson 10.2 Name Date Play Ball! Adding and Subtracting Polynomials Vocabulary Write the term from the box that best completes each statement. add combining like terms subtract distributive property 1. To calculate the sum of two polynomials, you must each group of like terms. 2. You can add or subtract polynomials by. For example, to calculate the sum of 3x 2 5x 6 and 8x 5x 2, you would add (3x 2 5x 2 ) (5x 8x) 6. 10 3. If you are subtracting one function from another function, you must each term of the second function from the first function. 4. To combine like terms, you can use the. For example, 5y 3y y(5 3) y(8) 8y. Problem Set Use the distributive property to simplify each expression. 1. 2x 10x 2x 10x x(2 10) x(12) 12x 2. 3x 7x 3. 17x 2 x 2 4. 31x 2 9x 2 5. 5x 2x 6. 8x 7x 7. x 5 19x 5 Chapter 10 Skills Practice 641
8. 13x 3 21x 3 9. 8x 2 7x 2 9x 2 10. 3x 2 11x 2 5x 2 Identify the like terms in each pair of polynomials. 0 11. (8x 9) (19 3x) 8x and 3x; 9 and 19 12. (11 12x) (6x 2) 13. 2x 2 4x 6 and 6x 2 20x 8 14. x 2 x 1 and 3x 2 9x 3 15. x 2 x 8 and x 2 7x 7 16. 4x 2 4x 1 and 9x 2 9x 9 17. 1 x 7x 2 3x 3 and 10x 3 4x 2 18x 8 18. x 3 11x 2 2x 20 and 90 3x 12x 2 63x 3 19. 27x 2 4x 3 4 6x and 6 27x 24x 2 6x 3 20. 9 11x 13x 2 x 3 and 13x 17x 3 13 2x 2 Add the polynomials. 21. (8x 4) (5x 3) (8x 4) (5x 3) (8x 5x) (4 3) 13x 7 22. (2x 9) (7x 2) 642 Chapter 10 Skills Practice
Name Date 23. (11x 2) (12 3x) 24. (16x 6) (19 2x) 25. (21x 2 6x 14) (x 2 3x 18) 26. (9x 2 9x 5) ( 23x 2 7x 21) 27. ( 3x x 2 1) (22x 2 3x 71) 28. (15x 2 30x 5) ( 41x 19x 2 5) 10 Subtract the polynomials. 29. (28x 7) (14x 6) (28x 7) (14x 6) (28x 14x) (7 6) 14x 1 30. (30x 20) (17x 17) 31. (6x 5) (12x 6) 32. (15x 14) (45x 31) 33. (3x 2 8x 24) (9x 2 21x 12) 34. (5x 2 10x 5) (26x 2 27x 28) 35. ( x 2 21x 3) (91x 80 x 2 ) Chapter 10 Skills Practice 643
36. (60x 7x 2 13) (4x 2 3 42x) Simplify each expression by calculating the sum or difference. 37. (8x 2 17x 6) ( 12x 2 15x 8) (8x 2 17x 6) ( 12x 2 15x 8) (8x 2 12x 2 ) ( 17x 15x) (6 8) 20x 2 32x 2 38. (30x 2 4x 20) ( 35x 2 x 24) 0 39. (3 x 2 11x) (9x 8 31x 2 ) 40. (12x 3x 2 1) (6x 2 15 2x) 41. (2x 3x 2 16) (x 2 15) 42. (18 7x 7x 2 ) (20x 5) 43. (8x 3 3x 2) ( x 2 9x 10) 44. ( 6x 3 x 2 x) (4x 3 4x 2 16) 45. (7x 2 11x 3 20) ( 2x 2 x 8) 46. (6x 2 3x 3 3x) (10x 2x 3 6) 644 Chapter 10 Skills Practice
Skills Practice Skills Practice for Lesson 10.3 Name Date Se Habla Español Multiplying and Dividing Polynomials Vocabulary Provide an example of each term below. 1. distributive property 10 2. divisor 3. dividend 4. remainder 5. area model Chapter 10 Skills Practice 645
Problem Set Use an area model to multiply the polynomials. 1. (3x 1)(2x 2) 2. (2x 4)(3x) 2x + 2 x x 1 1 3x + 1 x x x 1 6x 2 8x 2 3. (4x 2)(4x 1) 4. (5x 1)(x 4) 0 Use the distributive property to multiply the polynomials. 5. (2x)(2x 7) (2x)(2x 7) (2x)(2x) (2x)(7) 4x 2 14x 6. (3x)(x 5) 7. (9x 2 )(3x 8) 8. (7x 2 )(6x 4) 646 Chapter 10 Skills Practice
Name Date 9. (2x 3)(7x 11) 10. (3x 2)(8x 6) 11. (x 2 5)(20x 17) 10 12. (12x 2 14x)(x 4) 13. (x 4)(x 2 8x 16) 14. (x 5)(2x 2 3x 4) Chapter 10 Skills Practice 647
Use long division to divide the polynomials. 15. (x 2 10x 16) (x 2) 16. (x 2 5x 6) (x 3) x 8 x 2 ) x 2 10x 16 x 2 2x 8x 16 8x 16 0 0 17. (2x 3 13x 2 9x 22) (x 6) 18. (6x 3 19x 2 12x 2) (2x 5) 19. (8x 2 10x 6) (2x 7) 20. (9x 2 15x 15) (3x 3) 21. (8x 3 6x 2 40) (2x 6) 22. (12x 3 16x 14) (4x 8) 648 Chapter 10 Skills Practice
Skills Practice Skills Practice for Lesson 10.4 Name Date Making Stained Glass Multiplying Binomials Vocabulary Provide an example of each term below. 1. FOIL pattern 2. square of a binomial sum 10 3. square of a binomial difference Problem Set Use the FOIL pattern to calculate each product. 1. (x 6)(x 3) (x 6)(x 3) x 2 3x 6x 18 x 2 9x 18 2. (x 4)(x 5) 3. (x 1)(2x 4) 4. (3x 7)(x 2) 5. (5x 1)(x 4) 6. (x 8)(6x 2) 7. (x 10)(x 4) Chapter 10 Skills Practice 649
8. (x 3)(x 9) 9. (13x 1)(3x 13) 10. (12x 4)(x 8) 0 Use the FOIL pattern to calculate the square of each binomial sum. 11. (x 5) 2 (x 5) 2 (x 5)(x 5) x 2 5x 5x 25 x 2 10x 25 12. (x 3) 2 13. (x 8) 2 14. (x 10) 2 15. (x 13) 2 16. (x 11) 2 17. (x 12) 2 18. (x 15) 2 19. (x 30) 2 20. (x 40) 2 650 Chapter 10 Skills Practice
Name Date Use the FOIL pattern to calculate the square of each binomial difference. 21. (x 2) 2 (x 2) 2 (x 2)(x 2) x 2 2x 2x 4 x 2 4x 4 22. (x 1) 2 23. (x 6) 2 24. (x 4) 2 10 25. (x 9) 2 26. (x 7) 2 27. (x 11) 2 28. (x 13) 2 29. (x 14) 2 30. (x 16) 2 Use the FOIL pattern to calculate each product. 31. (x 3)(x 3) (x 3)(x 3) x 2 3x 3x 9 x 2 9 32. (x 5)(x 5) 33. (x 11)(x 11) Chapter 10 Skills Practice 651
34. (x 8)(x 8) 35. (2x 6)(2x 6) 36. (5x 3)(5x 3) 37. (14x 2)(14x 2) 0 38. (12x 7)(12x 7) 39. (8 9x)(8 9x) 40. (11 7x)(11 7x) 652 Chapter 10 Skills Practice
Skills Practice Skills Practice for Lesson 10.5 Name Date Suspension Bridges Factoring Polynomials Vocabulary Write the term from the box that best completes each statement. factor FOIL pattern linear factor trinomial 1. The number 2 is a of both the number 8 and the binomial 6x 20. 2. The sign of the constant in a determines the signs of the constants in its linear factors. 10 3. The can be used to quickly calculate the product of two polynomials. For instance, (2x 1) (x 9) (2x)(x) (2x)(9) (1)(x) (1)(9). 4. The expression x 2 is a of the expression x 2 4x 4. Problem Set Factor each expression completely. 1. x 2 2x x 2 2x x(x) x(2) x(x 2) 2. 4x x 2 3. 3x 2 4x 4. 2x 3 5x 5. 6x 2 8x 4 6. 9x 7 24x 4 7. 25x 3 15 Chapter 10 Skills Practice 653
8. 18x 2 36 Factor each trinomial as a product of linear factors. Then use the FOIL pattern to verify your answer. 9. x 2 12x 36 x 2 12x 36 (x 6) 2 Check: 10. x 2 8x 16 0 (x 6)(x 6) x 2 12x 36 11. x 2 14x 49 12. x 2 22x 121 13. x 2 16x 64 14. x 2 20x 100 15. x 2 140x 4900 16. x 2 100x 2500 Factor each trinomial as a product of linear factors. Then use the FOIL pattern to verify your answer. 17. x 2 9 x 2 9 (x 3)(x 3) Check: (x 3)(x 3) x 2 3x 3x 9 x 2 9 18. x 2 4 19. x 2 25 654 Chapter 10 Skills Practice
Name Date 20. x 2 81 21. x 2 144 22. x 2 400 10 23. 9x 2 8100 24. 16x 2 256 Factor each trinomial as a product of linear factors. Then use the FOIL pattern to verify your answer. 25. x 2 13x 42 x 2 13x 42 (x 6)(x 7) Check: (x 6)(x 7) x 2 7x 6x 42 x 2 13x 42 26. x 2 13x 36 Chapter 10 Skills Practice 655
27. x 2 21x 110 28. x 2 19x 90 0 29. x 2 11x 60 30. x 2 18x 40 31. x 2 3x 108 32. x 2 10x 39 Factor each trinomial as a product of linear factors. Then use the FOIL pattern to verify your answer. 33. 2x 2 17x 21 2x 2 17x 21 (2x 3)(x 7) Check: (2x 3)(x 7) 2x 2 14x 3x 21 2x 2 17x 21 656 Chapter 10 Skills Practice
Name Date 34. 5x 2 21x 4 35. 8x 2 22x 15 36. 6x 2 27x 21 10 37. 35x 2 177x 220 38. 55x 2 104x 48 39. 102x 2 201x 75 40. 195x 2 125x 20 Chapter 10 Skills Practice 657
0 658 Chapter 10 Skills Practice
Skills Practice Skills Practice for Lesson 10.6 Name Date Swimming Pools Rational Expressions Vocabulary Write the term from the box that best completes each statement. rational expression restricting the domain excluded or restricted value domain 1. The of an expression is all possible values of x so that either the expression is a real number or the value of x makes sense in a real-life situation. 2. A(n) is a fraction that contains an algebraic expression in the numerator, the denominator, or both. 10 3. is a process of eliminating excluded values from the domain of a rational expression. 4. A(n) is a value of the variable that results in a zero in the denominator of a rational expression. Problem Set Identify the excluded value(s) for each rational expression. 1. x 9 x 3 x 3 2. x 10 x 5 3. 5. 3x x 2 9x 3x x 2 8x 20 4. 6. 8x x 2 x 2x 1 x 2 x 12 Simplify each rational expression completely. Be sure to include excluded values. 7. 2 x 2 2x x 2 2x 3 2 x 2 2x x 2 2x 3 2x(x 1) (x 1)(x 3) 2x x 3 x 3, 1 Chapter 10 Skills Practice 659
8. 3 x 3 12 x 2 x 2 2x 8 9. x 2 15x 34 3 x 2 12 0 10. 4 x 2 484 x 2 8x 33 11. 3 x 4 12 x 3 12 x 2 6 x 3 108 x 2 240x 12. 8 x 12 16 x 11 280 x 10 5 x 4 50 x 3 125 x 2 660 Chapter 10 Skills Practice
Name Date Determine each product or quotient. Write your answer in simplest form and be sure to include excluded values. 13. ( x 2 (x 1) )( x 1 2 2x ) ( x 2 (x 1 ) )( x 1 2 2x ) x 2, x 0, 1 2x(x 1) x 4 )( x 1 14. ( 4x x 2 ) 10 15. ( x2 4x x 5 ) ( x2 3x 10 x 4 ) 16. ( 1 x 7 ) x 7 ) ( 2 x 2 17. 18. 2x 1 2x 1 4x 7 x 6 x 2 3x x 6 2x Chapter 10 Skills Practice 661
Determine each sum or difference. Write your answer in simplest form and be sure to include excluded values. 19. x x 2 2 x 2 x x 2 2 x 2 x 2 x 2, x 2 20. 7x x 4 1 x 4 0 21. 1 2x x 4 22. x 1 2 1 2x 23. 1 6 3 x 5 24. 3x 7 x 1 x 662 Chapter 10 Skills Practice